Filtrated K-theory for real rank zero C*-algebras

Sara Esther Arklint; Gunnar Restorff; Efren Ruiz

doi:10.1142/S0129167X12500784

Filtrated K-theory for real rank zero C*-algebras

Sara Esther Arklint, Gunnar Restorff, Efren Ruiz

Department of Mathematical Sciences

5 Citations (Scopus)

Abstract

The smallest primitive ideal spaces for which there exist counterexamples to the classification of non-simple, purely infinite, nuclear, separable C*-algebras using filtrated K-theory, are four-point spaces. In this article, we therefore restrict to real rank zero C*-algebras with four-point primitive ideal spaces. Up to homeomorphism, there are ten different connected T0-spaces with exactly four points. We show that filtrated K-theory classifies real rank zero, tight, stable, purely infinite, nuclear, separable C*-algebras that satisfy that all simple subquotients are in the bootstrap class for eight out of ten of these spaces.

Original language	English
Article number	1250078
Journal	International Journal of Mathematics
Volume	23
Issue number	8
Number of pages	19
ISSN	0129-167X
DOIs	https://doi.org/10.1142/S0129167X12500784
Publication status	Published - 13 Jun 2012

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Cite this

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AB - The smallest primitive ideal spaces for which there exist counterexamples to the classification of non-simple, purely infinite, nuclear, separable C*-algebras using filtrated K-theory, are four-point spaces. In this article, we therefore restrict to real rank zero C*-algebras with four-point primitive ideal spaces. Up to homeomorphism, there are ten different connected T0-spaces with exactly four points. We show that filtrated K-theory classifies real rank zero, tight, stable, purely infinite, nuclear, separable C*-algebras that satisfy that all simple subquotients are in the bootstrap class for eight out of ten of these spaces.

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